Almost Sure Synchronization Of Stochastic Complex Networks Driven By Lévy Process

Complex networks have been widely used in various disciplines and fields,such as biology,physics,social sciences,finance and other fields.Synchronization,as a very popular topic in complex network research in the past 10 years,has attracted a lot of researchers' attention and there have been a lot of results about various synchronization mode problems.When studying synchronization problems,considering noise in the system has become an indispensable part,and most scholars only consider Brownian motion as noise in the system.In practice,systems are often affected by abrupt factors,and Brownian motion can only be used to describe continuous noise.Hence,Lévy noise,a more general noise,needs to be considered to avoid this situation.It will be more significant in studying synchronization of complex stochastic networks.In addition,based on the needs of practical applications,the almost sure synchronization will be more meaningful than the mean square synchronization.So this dissertation considers the almost sure synchronization problem of stochastic networks which is driven by Lévy process.The main work of this paper includes the following:Firstly,the research background and current situation of complex networks are expounded.Then the related definitions about almost sure synchronization,the stochastic process theories,the related symbol definitions and lemmas are introduced.Secondly,the almost sure synchronization problem of nonlinear stochastic complex networks with Lévy process noise is discussed.The Markov chain is introduced to simulate the switching phenomenon of the system.Combining the designed adaptive feedback controller,the Lyapunov stability theory,the generalized It? integral of the Lévy process and the non-negative semi-convergence convergence theorem and so on,the sufficient conditions of almost sure synchronization about the class networks will be obtained.Numerical simulations are given by Matlab to verify the validity of the conclusion.Then,under a decentralized event-triggered sampling strategy,the almost sure synchronization problem of Markov switching networks with partial unknown transfer rate and Lévy noise is studied.By designing a decentralized event-triggered sampling control,and considering the situation that the transition rates of Markov chain is unknown partially,then,using stochastic process theories,Lyapunov stability theorem and other knowledge,the two cases of undirected network and directed network are discussed respectively.Under the decentralized event-triggered sampling strategy,the sufficient conditions which can make the Markov switching networks achieve synchronization almost surely is obtained.At the same time,the lower bound of the triggered interval of the strategy is calculated,which can avoid Zeno behavior.Then three numerical examples are given to verify the validity of the theorem in this chapter.Finally,under a concentrated event-triggered sampling strategy,the almost sure cluster synchronization problem with Lévy noise and Markov switching networks is considered.By designing a centralized event-triggered sampling strategy which will not cause the situation of Zeno behavior,and constructing a new stochastic Lyapunov-Krasovskii function,using the relevant stochastic process knowledge,the sufficient conditions of almost sure cluster synchronization for undirected and directed networks will be obtained.The result is also verified by simulation examples.